Robert Wilfred Levick Simpson (2 March 1921 – 21 November 1997) was an English composer and long-serving BBC producer and broadcaster.

He is best known for his orchestral and chamber music (including 11 symphonies and 15 string quartets), and for his writings on the music of Beethoven, Bruckner, Nielsen and Sibelius. He studied composition under Herbert Howells. Remarkably for a composer who was still alive, a Robert Simpson Society was formed in 1980 by individuals concerned that Simpson's music was unfairly neglected. The Society works to bring Simpson's music to a wider public by sponsoring recordings and live performances of his work, by issuing a journal and other publications, and by maintaining an archive.